MathDB

A concurrency with excenters

Source: Kürschák 1990, problem 2

July 20, 2014

geometryincentertrigonometryratioangle bisectortrig identitiesLaw of Sines

Problem Statement

The incenter of

\triangle A_1A_2A_3

I

, and the center of the

A_i

-excircle is

J_i

(

i=1,2,3

). Let

B_i

be the intersection point of side

A_{i+1}A_{i+2}

and the bisector of

\angle A_{i+1}IA_{i+2}

(

A_{i+3}:=A_i

\forall i

). Prove that the three lines

B_iJ_i

are concurrent.